Problem 11 - Prealgebra

Question

SAVINGS Chris is saving money to buy a stereo. He has \(\$ 62.50\), but his goal is to save at least \(\$ 100 .\) What is the least amount Chris still needs to save to reach his goal?

Step-by-Step Solution

Answer

Chris needs to save at least $37.50 more.

Step 1: Understand the Problem

Chris has $62.50 and his goal is to save at least $100. We need to find out how much more he needs to save to reach this goal.

Step 2: Set Up the Equation

Represent what Chris needs to save as an equation. Let the variable \( x \) be the amount Chris still needs to save. The equation will be: \( 62.50 + x = 100 \).

Step 3: Solve for the Variable

To find \( x \), we need to isolate it by performing arithmetic operations on the equation. Subtract 62.50 from both sides of the equation: \( x = 100 - 62.50 \).

Step 4: Calculate the Result

Perform the subtraction: \(100 - 62.50 = 37.50\). This means that Chris needs to save an additional \(\$ 37.50\).

Key Concepts

Understanding Your Savings Goal

Setting a savings goal is a crucial first step towards successful financial planning. It helps you focus on a target and emphasizes the importance of disciplined saving. In this case, Chris has a clear goal: to save at least $100 to buy a stereo. But why is setting such a goal important? - **Motivation:** Clearly defined goals keep you motivated, even when challenges arise. Knowing the end game gives every small saving or investment meaning. - **Measure of Progress:** Goals help measure progress over time. As Chris saves more money, he gets closer to his objective, which provides a sense of achievement. - **Financial Security:** Long-term goals encourage habit formation that leads to financial stability. It's not just about having a goal, but also making it specific and achievable. Chris knows he already has $62.50, so he only needs $37.50 more to reach his target.

Step-by-Step Problem Solving

Breaking down a problem into manageable steps is an effective way to ensure nothing is overlooked. Let's examine how to approach Chris's situation using a structured method:- **Step 1:** Understand the problem. It's essential to know what you're tackling. Chris wants to know how much more he has to save in order to buy his stereo.- **Step 2:** Set up an equation that represents the problem. Define a variable for the unknown quantity. In this scenario, let \( x \) be the missing amount Chris needs. - The equation: \( 62.50 + x = 100 \)- **Step 3:** Solve for the variable. Apply arithmetic operations to isolate \( x \). Subtract \(62.50 from \)100, leading to the conclusion that \( x = 100 - 62.50 \).- **Step 4:** Calculate the result. By performing the subtraction, we find that \( x = 37.50 \).Step-by-step problem solving avoids confusion and provides a clear path to finding solutions. It’s not just useful in savings calculations but applicable in all aspects of problem-solving.

Mastering Arithmetic Operations

Arithmetic operations, such as addition and subtraction, form the foundation of most math problems. Understanding these basics is essential.**Addition and Subtraction:**- **Addition:** Combines two quantities. In expressions like \( a + b \), you're merging their values. For Chris, adding \(62.50 and \( x \) equals his savings goal.- **Subtraction:** Helps determine the difference between quantities. This operation was critical in solving Chris's savings equation, where we subtracted \)62.50 from \(100.Here's how you apply these operations in a practical scenario:- **Example:** "If I have \)20 and spend $5, how much is left?" - Perform the subtraction: \( 20 - 5 = 15 \).Understanding when and how to use these operations is essential for daily tasks, from shopping to budgeting. In Chris’s case, effectively using subtraction revealed exactly how much more he needs to save, bringing clarity to his financial picture.